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Simplifying n2 + 19n + -60 = 0 Reorder the terms: -60 + 19n + n2 = 0 Solving -60 + 19n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 19n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + 19n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 19n + n2 = 0 + 60 19n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 19n + n2 = 60 The n term is 19n. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19n + 90.25 + n2 = 60 + 90.25 Reorder the terms: 90.25 + 19n + n2 = 60 + 90.25 Combine like terms: 60 + 90.25 = 150.25 90.25 + 19n + n2 = 150.25 Factor a perfect square on the left side: (n + 9.5)(n + 9.5) = 150.25 Calculate the square root of the right side: 12.257650672 Break this problem into two subproblems by setting (n + 9.5) equal to 12.257650672 and -12.257650672.Subproblem 1
n + 9.5 = 12.257650672 Simplifying n + 9.5 = 12.257650672 Reorder the terms: 9.5 + n = 12.257650672 Solving 9.5 + n = 12.257650672 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = 12.257650672 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = 12.257650672 + -9.5 n = 12.257650672 + -9.5 Combine like terms: 12.257650672 + -9.5 = 2.757650672 n = 2.757650672 Simplifying n = 2.757650672Subproblem 2
n + 9.5 = -12.257650672 Simplifying n + 9.5 = -12.257650672 Reorder the terms: 9.5 + n = -12.257650672 Solving 9.5 + n = -12.257650672 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = -12.257650672 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = -12.257650672 + -9.5 n = -12.257650672 + -9.5 Combine like terms: -12.257650672 + -9.5 = -21.757650672 n = -21.757650672 Simplifying n = -21.757650672Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.757650672, -21.757650672}
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